Concatenations x^2 || 3^2 = y^2

 
Here are the first few solutions to   x^2 \; || \; 3^2 \; = \; y^2

 

7^2 \; = \; 49 \; = \; 4 \; || \; 9 \; = \; 2^2 \; || \; 3^2

57^2 \; = \; 3249
18^2 \; = \; 324                    57^2 \; = \; 18^2 \; || \; 3^2

253^2 \; = \; 64009
  80^2 \; = \; 6400

253^2 \; = \; 80^2 \; || \; 3^2

487^2 \; = \; 237169
154^2 \; = \; 23716

487^2 \; = \; 154^2 \; || \; 3^2

2163^2 \; = \; 4678569
  684^2 \; = \; 467856

2163^2 \; = \; 684^2 \; || \; 3^2

9607^2 \; = \; 92294449
3038^2 \; = \; 9229444

9607^2 \; = \; 3038^2 \; || \; 3^2

82137^2 \; = \; 6746486769
25974^2 \; = \; 674648676

82137^2 \; = \; 25974^2 \; || \; 3^2

364813^2 \; = \; 133088524969
115364^2 \; = \; 13308852496

364813^2 \; = \; 115364^2 \; || \; 3^2

3119043^2 \; = \; 9728429235849
  986328^2 \; = \; 972842923584

3119043^2 \; = \; 986328^2 \; || \; 3^2

13853287^2 \; = \; 191913560704369
  4380794^2 \; = \; 19191356070436

13853287^2 \; = \; 4380794^2 \; || \; 3^2

118441497^2 \; = \; 14028388211601009
  37454490^2 \; = \; 1402838821160100

118441497^2 \; = \; 37454490^2 \; || \; 3^2

526060093^2 \; = \; 276739221447168649
166354808^2 \; = \; 27673922144716864

526060093^2 \; = \; 166354808^2 \; || \; 3^2

4497657843^2 \; = \; 20228926072699412649
1422284292^2 \; = \; 2022892607269941264

4497657843^2 \; = \; 1422284292^2 \; || \; 3^2

19976430247^2 \; = \; 399057765413256481009
  6317101910^2 \; = \; 39905776541325648100

19976430247^2 \; = \; 6317101910^2 \; || \; 3^2

170792556537^2 \; = \; 29170097368444341432369
  54009348606^2 \; = \; 2917009736844434143236

170792556537^2 \; = \; 54009348606^2 \; || \; 3^2

758578289293^2 \; = \; 575441020986694398439849
239883517772^2 \; = \; 57544102098669439843984

758578289293^2 \; = \; 239883517772^2 \; || \; 3^2

6485619490563^2 \; = \; 42063260176370667646056969
2050932962736^2 \; = \; 4206326017637066764605696

6485619490563^2 \; = \; 2050932962736^2 \; || \; 3^2

28805998562887^2 \; = \; 829785553205047909293774769
  9109256573426^2 \; = \; 82978555320504790929377476

28805998562887^2 \; = \; 9109256573426^2 \; || \; 3^2

246282748084857^2 \; = \; 60655192004229134301272710449
  77881443235362^2 \; = \; 6065519200422913430127271044

246282748084857^2 \; = \; 77881443235362^2 \; || \; 3^2

1093869367100413^2 \; = \; 1196550192280658098507224770569
  345911866272416^2 \; = \; 119655019228065809850722477056

1093869367100413^2 \; = \; 345911866272416^2 \; || \; 3^2

9352258807734003^2 \; = \; 87464744806838235291767602404009
2957443909981020^2 \; = \; 8746474480683823529176760240400

9352258807734003^2 \; = \; 2957443909981020^2 \; || \; 3^2

41538229951252807^2 \; = \; 1725424547483155772999508825379249
13135541661778382^2 \; = \; 172542454748315577299950882537924

41538229951252807^2 \; = \; 13135541661778382^2 \; || \; 3^2

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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